inference rule
In logic, an inference rule is a rule whereby one may correctlydraw a conclusion from one or more premises. For example, the law ofthe contrapositive allows one to conclude a statement of the form
from a premise of the form
Here, ‘’ and ‘’ are propositional variables, which can stand forarbitrary propositions. A popular way to indicate applications of rulesof inference is to list the premises above a line and write theconclusions below the line. For instance, we might indicate the lawof the contrapositive thus:
A typical application of the law ofcontrapositive would be to conclude ”If my clothes are dry, then it is notraining”, from ”If it rains, then my clothes will be wet.” which could beexpressed as follows using the notation described above:
(In thisinstance, is “It is raining” and is “My clothes are dry”.
An important feature of rules of inference is that they are purely formal,which means that all that matters is the form of the expression;meaning is not a consideration in applying a rule of inference.Thus, the following are equally valid applications of the rule ofthe contrapositive:
In the first example, the statements are nonsense and in the secondexample, the statements are false, but this doesn’t matter — bothexamples constitute valid apllications of the rule of the contrapositive.Of course, in order to draw valid conclusions, we need to start withvalid premises, but the point of these examples is clarify thedistinction between valid statements and valid applications ofrules of inference.
Title | inference rule |
Canonical name | InferenceRule |
Date of creation | 2013-03-22 16:50:51 |
Last modified on | 2013-03-22 16:50:51 |
Owner | rspuzio (6075) |
Last modified by | rspuzio (6075) |
Numerical id | 8 |
Author | rspuzio (6075) |
Entry type | Definition |
Classification | msc 03B35 |
Classification | msc 03B22 |
Classification | msc 03B05 |
Synonym | rule of inference |
Related topic | ModusPonens |
Related topic | LogicalAxiom |
Related topic | DeductiveSystem |